1 /*
2 * Single-precision vector tan(x) function.
3 *
4 * Copyright (c) 2021-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "v_math.h"
9 #include "estrinf.h"
10 #include "pl_sig.h"
11 #include "pl_test.h"
12
13 #if V_SUPPORTED
14
15 /* Constants. */
16 #define NegPio2_1 (v_f32 (-0x1.921fb6p+0f))
17 #define NegPio2_2 (v_f32 (0x1.777a5cp-25f))
18 #define NegPio2_3 (v_f32 (0x1.ee59dap-50f))
19 #define InvPio2 (v_f32 (0x1.45f306p-1f))
20 #define RangeVal (0x47000000) /* asuint32(0x1p15f). */
21 #define TinyBound (0x30000000) /* asuint32 (0x1p-31). */
22 #define Shift (v_f32 (0x1.8p+23f))
23 #define AbsMask (v_u32 (0x7fffffff))
24
25 #define poly(i) v_f32 (__tanf_poly_data.poly_tan[i])
26
27 /* Special cases (fall back to scalar calls). */
28 VPCS_ATTR
29 NOINLINE static v_f32_t
specialcase(v_f32_t x,v_f32_t y,v_u32_t cmp)30 specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
31 {
32 return v_call_f32 (tanf, x, y, cmp);
33 }
34
35 /* Use a full Estrin scheme to evaluate polynomial. */
36 static inline v_f32_t
eval_poly(v_f32_t z)37 eval_poly (v_f32_t z)
38 {
39 v_f32_t z2 = z * z;
40 #if WANT_SIMD_EXCEPT
41 /* Tiny z (<= 0x1p-31) will underflow when calculating z^4. If fp exceptions
42 are to be triggered correctly, sidestep this by fixing such lanes to 0. */
43 v_u32_t will_uflow = v_cond_u32 ((v_as_u32_f32 (z) & AbsMask) <= TinyBound);
44 if (unlikely (v_any_u32 (will_uflow)))
45 z2 = v_sel_f32 (will_uflow, v_f32 (0), z2);
46 #endif
47 v_f32_t z4 = z2 * z2;
48 return ESTRIN_5 (z, z2, z4, poly);
49 }
50
51 /* Fast implementation of Neon tanf.
52 Maximum error is 3.45 ULP:
53 __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
54 want 0x1.ff9850p-1. */
55 VPCS_ATTR
V_NAME(tanf)56 v_f32_t V_NAME (tanf) (v_f32_t x)
57 {
58 v_f32_t special_arg = x;
59 v_u32_t ix = v_as_u32_f32 (x);
60 v_u32_t iax = ix & AbsMask;
61
62 /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
63 regression. */
64 #if WANT_SIMD_EXCEPT
65 /* If fp exceptions are to be triggered correctly, also special-case tiny
66 input, as this will load to overflow later. Fix any special lanes to 1 to
67 prevent any exceptions being triggered. */
68 v_u32_t special = v_cond_u32 (iax - TinyBound >= RangeVal - TinyBound);
69 if (unlikely (v_any_u32 (special)))
70 x = v_sel_f32 (special, v_f32 (1.0f), x);
71 #else
72 /* Otherwise, special-case large and special values. */
73 v_u32_t special = v_cond_u32 (iax >= RangeVal);
74 #endif
75
76 /* n = rint(x/(pi/2)). */
77 v_f32_t q = v_fma_f32 (InvPio2, x, Shift);
78 v_f32_t n = q - Shift;
79 /* n is representable as a signed integer, simply convert it. */
80 v_s32_t in = v_round_s32 (n);
81 /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
82 v_s32_t alt = in & 1;
83 v_u32_t pred_alt = (alt != 0);
84
85 /* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */
86 v_f32_t r;
87 r = v_fma_f32 (NegPio2_1, n, x);
88 r = v_fma_f32 (NegPio2_2, n, r);
89 r = v_fma_f32 (NegPio2_3, n, r);
90
91 /* If x lives in an interval, where |tan(x)|
92 - is finite, then use a polynomial approximation of the form
93 tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
94 - grows to infinity then use symmetries of tangent and the identity
95 tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
96 the same polynomial approximation of tan as above. */
97
98 /* Perform additional reduction if required. */
99 v_f32_t z = v_sel_f32 (pred_alt, -r, r);
100
101 /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
102 v_f32_t z2 = r * r;
103 v_f32_t p = eval_poly (z2);
104 v_f32_t y = v_fma_f32 (z * z2, p, z);
105
106 /* Compute reciprocal and apply if required. */
107 v_f32_t inv_y = v_div_f32 (v_f32 (1.0f), y);
108 y = v_sel_f32 (pred_alt, inv_y, y);
109
110 /* Fast reduction does not handle the x = -0.0 case well,
111 therefore it is fixed here. */
112 y = v_sel_f32 (x == v_f32 (-0.0), x, y);
113
114 if (unlikely (v_any_u32 (special)))
115 return specialcase (special_arg, y, special);
116 return y;
117 }
118 VPCS_ALIAS
119
120 PL_SIG (V, F, 1, tan, -3.1, 3.1)
121 PL_TEST_ULP (V_NAME (tanf), 2.96)
122 PL_TEST_EXPECT_FENV (V_NAME (tanf), WANT_SIMD_EXCEPT)
123 PL_TEST_INTERVAL (V_NAME (tanf), -0.0, -0x1p126, 100)
124 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-149, 0x1p-126, 4000)
125 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-126, 0x1p-23, 50000)
126 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-23, 0.7, 50000)
127 PL_TEST_INTERVAL (V_NAME (tanf), 0.7, 1.5, 50000)
128 PL_TEST_INTERVAL (V_NAME (tanf), 1.5, 100, 50000)
129 PL_TEST_INTERVAL (V_NAME (tanf), 100, 0x1p17, 50000)
130 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p17, inf, 50000)
131 #endif
132